This proposal is in response to the Funding Opportunity Announcement PAR- 11-032 on Methods and Approaches for Detection of Gene- Environment Interactions in Human Disease (R21). The proposal will be led by multiple PIs, Dr. Bhramar Mukherjee at the Department of Biostatistics, University of Michigan and Dr. Jinbo Chen at the Department of Biostatistics and Epidemiology, University of Pennsylvania. Dr. Stephen B. Gruber, Dr. Sung Kyun Park and Dr. Naisyin Wang from the University of Michigan are key clinical and methodological consultants on the project. In this proposal, we will have two specific aims: (i) Evaluate efficient two-phase design and analysis choices in the post genomewide association studies (GWAS) era where additional genotyping or biomarker data is collected on a prioritized selection of a sub-sample of study subjects in an existing study base. This includes the possibility of using supplementary data on cases and controls with only genetic or environmental data. The methods are guided by modern retrospective likelihood framework. (ii) Develop methods for screening of interaction in cohort studies using a novel technique developed by the PIs called Principal Interactions Analysis. This method is based on a parsimonious low rank representation of the interaction matrix after fitting additive main effects of gene and environment. The proposal plans to extend this method to longitudinal studies to capture time- varying effects of interaction. Visual diagnostics to identify time-windows of critical importance will be developed as a byproduct. The planned work in this important proposal will meaningfully contribute to the mission of this FOA, and advance study design and analytical techniques for studying G x E effects. The proposal will involve active collaboration between Dr. Chen and Dr. Mukherjee, their doctoral/post-doctoral trainees and foster collaboration between two peer institutions: University of Pennsylvania and University of Michigan. The proposal lies in the intersection of statistics, medicine, epidemiology and human genetics in terms of methodology development. The broader impact is better understanding of disease etiology and identify potentials for targeted intervention strategies.